论文标题
边界稳定在一维线性双曲线平衡定律的有限时间内，其系数取决于时间和空间
Boundary stabilization in finite time of one-dimensional linear hyperbolic balance laws with coefficients depending on time and space
论文作者
论文摘要
在本文中，我们对在一维线性双曲线平衡定律的有限时间内具有系数，其系数取决于时间和空间感兴趣。我们通过引入适当的时间依赖性积分转换来扩展所谓的“反击方法”，以将我们的初始系统映射到具有所需稳定性属性的新系统。所涉及的积分转换的内核是对非标准多维双曲线PDE的解决方案，在这种情况下，时间依赖性在治疗其适当性良好时引入了一些新的困难。这项工作概括了文献的先前结果，其中仅考虑时间独立的系统。
In this article we are interested in the boundary stabilization in finite time of one-dimensional linear hyperbolic balance laws with coefficients depending on time and space. We extend the so called "backstepping method" by introducing appropriate time-dependent integral transformations in order to map our initial system to a new one which has desired stability properties. The kernels of the integral transformations involved are solutions to non standard multi-dimensional hyperbolic PDEs, where the time dependence introduces several new difficulties in the treatment of their well-posedness. This work generalizes previous results of the literature, where only time-independent systems were considered.
